The incapacitation of South Dakota Senator Tim Johnson has put all eyes in Washington on what is normally a little-noticed Senate vote now scheduled for Jan. 4. It is called the "organizing resolution," and is the bit of internal housekeeping that determines how committee memberships will be allotted between the two parties, as well as who will get to serve as chairman and ranking members of each of the panels. These resolutions traditionally stand until the next Congress, even if the makeup of the chamber shifts to put the other party in the majority, which is why precedent would seem to dictate that the Chamber would stay in Democratic hands, even if Johnson is replaced by a Republican.

But don't count on it this time. Incoming majority leader Harry Reid insisted at a press conference that "there isn't a thing that's changed" as a result of Johnson's illness. But a family friend told TIME.com Thursday morning that Johnson's prognosis is unclear, adding: "The next 24 hours will be crucial."

Even if Johnson ultimately recovers from the congenital blood disorder known as arteriovenous malformation, which required emergency surgery Wednesday night, it now looks highly unlikely that he will healthy by Jan. 4. With Johnson unable to vote, Democrats still have enough to prevail, with 50 votes (including the two independent Senators, Joe Lieberman of Connecticut and Bernie Sanders of Vermont) to 49 for the Republicans. But Democrats now fear the real possibility that Republicans will filibuster that resolution. They could insist  just as the Democrats did after the 2000 election that left the chamber evenly split, with Vice President Dick Cheney as the tie-breaker  on an "out clause" that stipulates that control of the chamber goes to them if they somehow manage to achieve a majority during the course of the session. As both sides remember, that clause came in handy for the Democrats a few months later, when Vermont's Jim Jeffords abruptly declared himself an independent and gave the Democrats a one-vote majority.

The same thing could happen again, in a Senate currently split 51-49 in favor of the Democrats, if Johnson or any other Democrat were to be replaced by a Republican. In Johnson's case, that would appear likely, because his replacement would be named by a Republican governor. State law requires that Gov. Michael Rounds make a "temporary appointment, until a special election is held"  though it is unclear whether that election would occur before Johnson's term expires in 2008.

If the Republicans filibuster the organizing resolution and the question drags on into January or even beyond, it presents another truly extraordinary possibility: a chamber with a new Democratic leader, but the existing set of Republican committee chairmen. That is because, until an organizing resolution is passed, incoming Majority Leader Harry Reid would have no control over the committees.

The question of who runs the committees could have major policy implications. If Republicans took over, the chairman of the Senate Armed Services Committee, for example, would most likely be Arizona Republican John McCain, who advocates more troops in Iraq. If the Democrats retain control, it would be Michigan Democrat Carl Levin, who is arguing for a plan that would reduce the number there.